A generic attitude and orbit control system (AOCS) of spacecraft, for example satellites, is made up of kinematic AOCS sensors, software for determining the kinematic state (attitude and orbit determination (AOD)), software for targeted control of the state (attitude and orbit control (AOC)), and a number of AOCS actuators for implementing the control instructions.
Traditionally, the hardware for these AOCS elements is connected to a central computer of the aircraft, such as a satellite computer, on which the AOD and AOC software runs. Such a typical AOCS configuration is described in US 2003/009248 A1. The satellite computer uses the kinematic and dynamic state equations in order to control the satellite according to a given control law, using models of the sensors and actuators.
The rotational position, the rotational speed (also referred to as rotation rate), the rotational acceleration, as well as the corresponding translatory variables location, speed, and acceleration are used as kinematic variables. In addition, the parameters torque, moment of inertia, force, and mass are used in the dynamic equations.
AOCS sensors which are used are star sensors, solar sensors, earth sensors and magnetometers for the rotational position, gyroscopes for the rotation rate, global navigation satellite system (GNSS) sensors for the location, and acceleration sensors. In interferometric evaluation, GNSS sensors may likewise be used for detecting the rotational position with less accuracy.
The synergistic evaluation of the measured values from various kinematic AOCS sensors for data processing in attitude and orbit control systems is known from “Optimal Estimation for the Satellite Attitude Using Star Tracker Measurements,” James Ting-Ho Lo, 1978. For example, the data of three to six gyroscopes and two star sensors are used for joint position estimation. In the process, all measuring data are combined into a single data stream. Data buses, primarily according to the MIL 1553 standard, have become prevalent for distributing the data streams between multiple device units of the satellite. Thus, GEOS satellites (see “GEOS-N Data Book: 11. Attitude Control,” Boeing, February 2005) include a data bus according to MIL 1553, via which multiple star sensors and gyroscopes are connected to the electronics box of the attitude control system.
Initially, approaches were used having centralized evaluation of the AOCS sensor data in the satellite computer. This was essential and appropriate, since the low performance level of the sensors resulted in usable results only when multiple sensors, having a low data rate, were evaluated jointly. Examples of approaches to the problem of an insufficient number of stars detectable using a star sensor are described in U.S. Pat. No. 6,108,594 A and US 2003/0009284 A1, for example, in which centralized evaluation of the data of two star sensors in the satellite computer is necessary.
With the advent of small, powerful digital signal processors (DSP) and application-specific integrated circuit (ASIC) processing units, this resulted in the transition to decentralized processing in the sensors themselves.
At the present time, a reverse trend away from decentralization has begun. The reason lies in the fact that autonomous processing is not economically or energetically efficient, since recent processing units are overdimensioned with respect to their power for an individual sensor. In addition, in decentralized systems the opportunity is lost for synergies which are utilizable via the joint evaluation of complementary sensors.
Thus far, two trends have been observed in the decline in autonomous sensors: first, the return to centralized evaluation in the satellite computer, and second, the move toward integration of multiple types of sensors into a single hybrid sensor.
A prominent example of the first trend toward centralization is the transition from autonomous star sensors to star sensor heads, which are made up solely of a star camera and which do not have their own processing unit. The evaluation of the star data once again takes place in the satellite computer, using the star sensor software which is ported therein. However, this development has not been without problems. The star sensor is the most complex AOCS sensor, and the manufacturers' knowledge base which has been developed over decades is not easily transferable to the satellite manufacturers via software porting. In addition, the AOCS satellite bus, which is customarily used for connecting the satellite computer to the other AOCS elements, is overloaded by the quantity of unprocessed star sensor data. This is presently avoided by the additional use of point-to-point data connections in addition to the AOCS satellite bus. However, this entails increased mass and susceptibility to malfunction.
In U.S. Pat. No. 7,216,036 B2, the integration of the star sensor and the rotation rate gyroscope into a single device is used as a solution to the mentioned problems of centralization. According to the cited invention, the star camera data and gyroscope data are conducted in an internal, synchronously integrated data stream to the processing unit of the device (flight computer), where they are jointly processed and compressed. This once again allows data transmission over the standard AOCS bus of the satellite. However, the completely joint processing of gyroscope data and star sensor data does not solve the problem of integrating the knowledge base for gyroscopes and star sensors for a device manufacturer. The star sensor is used only as a secondary sensor, and its improved performance is not definitive for the system. Furthermore, there is the disadvantage that with respect to mass, volume, and heat output, the integrated device is unsuitable for an otherwise customary mounting on the sensitive primary instruments of the satellite. Thus, this approach is suitable only for small satellites having limited requirements.
The lack of control information of the AOC, which is available only in the central computer of the satellite, is considered by proponents of a return to centralized processing in the satellite computer as a process engineering drawback of decentralized approaches. The topology of the distribution and the combination of the processing units must also take into account the possibilities for subdividing the method steps.
As a counterargument to a return to centralized implementation of evaluation of measured values and satellite control in the satellite computer, other sources cite the difficulty in mastering the highly complex software necessary for this purpose.
In U.S. Pat. No. 8,056,863 B2, the aim is to reduce the complexity in the central computer by using unified measured value evaluations and control laws. A disadvantage of this approach is that only simple methods may be used, resulting in limitations for optimal control. In addition, the measured value evaluation and the satellite control must be coordinated very closely with one another. Thus, a limitation to low data rates, for example, is provided in the document U.S. Pat. No. 8,056,863 B2. This diminishes the options for an actual unification, in which approaches must be applicable to a broad class of satellites.
Practically all AOD methods are based on statistically optimized estimation methods. Depending on the complexity of the statistical model used, the methods are subdivided into least square root (LSR) methods, methods based on the maximum likelihood (ML) principle, and Bayesian methods. The statistical model describes the detection of the kinematic AOCS measuring data and the behavior of the satellite as two statistical Markov processes. Those parameters to be estimated for which the observed measured values appear to be most likely are assumed to be optimal. Since only the parameters involved in the measuring process may be directly observed, whereas the system behavior is indirectly derived, such a model is also referred to as a hidden Markov process model.
In the LSR method, statistical parameters are not known for either of the two processes, and all errors to be minimized are entered with the same weight into the optimization. If different error variances are known, for example for the three components of the position to be determined, the corresponding errors are weighted with the inverse variance in the optimization. This results in maximization of the likelihood. If the statistical parameters are not modeled as constant, but instead are themselves a static function of other parameters, the Bayesian estimator is optimal. Thus, the parameter dependencies must be regarded as probabilities which are known a priori, or additional models of the relationship between the parameters and the measured values must be introduced.
Since the parameter dependencies are usually unknown or difficult to estimate, in practice only LSR and ML methods, but not Bayesian estimators, are used in the AOCS.
The AOD and AOC processes run cyclically in the satellite, which suggests an implementation of the estimation methods as recursive filters, so-called Kalman filters (KF). The instantaneous optimal estimation is determined from the measured values of the present cycle and from the prediction made in the preceding cycle. Simply stated, an optimal time-variable compromise is found between measurement and prediction.
The KF methods have proven to be practical in many satellite missions, although some disadvantages are also known. The article “Nonlinear attitude filtering methods,” F. L. Markley et al., J. AIAA 2005, provides an overview of approaches to overcoming these disadvantages. The process equations for the kinematic and dynamic parameters of the satellite control are not linear. The Kalman filter presumes linearity. For this reason, the extended Kalman filter (EKF) has been developed, in which the nonlinear equations are linearly approximated. In addition to improvements, the EKF has resulted in new drawbacks with regard to convergence and stability. As a countermeasure, the unscented Kalman filter (UKF) was developed (see, for example, the publication “Unscented Kalman filtering for spacecraft attitude state and parameter estimation,” M. C. VanDyke, J. L. Schwartz, and C. D. Hall, in Proceedings, No. AAS-0115, 2004), in which the process equations are applied without linearization. The equations are applied to a quantity of supporting points of the statistical parameters randomly selected according to the Monte Carlo principle. For this purpose, the statistical distribution for these parameters must be known. A Gaussian distribution is usually assumed. The much larger quantity of data to be processed is disadvantageous. If the statistical distribution functions are unknown, which frequently is the case for AOCS applications, many more supporting points of the Monte Carlo method must be used in the so-called particle filter. This virtually completely eliminates the practical application of particle filters in the AOCS.
One alternative method for improving the KF methods is to combine them with so-called batch estimators. Not only are the measured and predictive values of the present cycle used, but also an entire “batch” of cycles is entered into the processing. The known batch methods result in smoothing of the results of the KF methods, and are carried out subsequent to same. Such smoothing of the KF result over multiple cycles is described in the article “Gyro Stellar Attitude Determination,” Mehdi Ghezal et al., Proceedings of the 6th International ESA Conference on Guidance, Navigation and Control Systems, Loutraki, Greece, Oct. 17-20, 2005.
The joint filtering of measured position values of the star sensor and measured rate values of the gyroscope sensor represents a particular challenge. As the most important measuring equipment, these two sensors form the core of the AOD system. The two types of sensors have greatly different properties, which potentially may be used for mutual assistance, but this also entails certain difficulties in the hybridization of their data. Gyroscope sensors have less noise, which allows a more accurate, but only relative, position measurement over short time periods. The drift and the scaling factor error, which become dominant over longer time periods, are problematic with gyroscope sensors. Star sensors have slightly more noise, and over fairly short time periods may be disabled by glare. However, they always provide an absolute position measurement, and do not drift. The above-cited article summarizes the results of the strategy of the synergistic fusion of data of the star sensor and the gyroscope. The article concludes that up until now, the parameter selection must be very specific to the particular mission. In practice, this is very difficult and involves a high level of additional complexity. In addition to the batch smoothing mentioned above, the above-cited article provides two further possible approaches to this problem.
The first approach lies in subdividing the satellite missions or mission phases into two categories: those with short-term joint position estimation, using data from the star sensor and the gyroscope (for example, during image recording by the primary instrument of the satellite), and those with good long-term behavior (for example, geostationary satellites or mission phases having a fixed orientation with respect to the sun).
For both categories, the filtering of the star sensor data and the gyroscope measurements takes place in a single Kalman filter having a certain hybridization frequency. In the short-term category, a high hybridization frequency is selected, while the long-term category requires a low frequency. In the short-term category, the star sensor is dominant, and with its noise and in particular its low-frequency error components determines the accuracy of the position measurement. The gyroscope parameters hardly play a role, and only very brief down times of the star sensor may be bridged with gyroscope data. The gyroscope need not be of high quality, as is the case for the long-term category. In the long-term scenario, the expensive gyroscope determines the accuracy, which is sufficiently good over a long period of time. The star sensor is present only for occasional drift compensation of the gyroscope, and its low-frequency error components do not play a role.
As the second approach, the article describes an additional test filter (consider filter). Parameters which actually may not be sufficiently well observed and which therefore may not be estimated are received in the Kalman filter. In this case, the three components of the scaling factor error are used as test parameters. Normally, only the gyroscope drift is estimated in the Kalman filter. The estimations for the scaling factor are not usable in the system equations; instead, they are used only for artificial degradation of the estimated error. The aim is to prevent the covariance of the position from being unjustifiably assessed as satisfactory, and to prevent the filter from causing disorientation of the satellite due to incorrect weights.
U.S. Pat. No. 7,216,036 B2 likewise describes a method corresponding to the long-term category of the star sensor-gyroscope hybridization. In this case, the strategy is not used for expensive, highly accurate gyroscopes, but instead is used for simple gyroscopes whose accuracy is sufficient for certain small satellite missions. The star sensor is used here only to compensate for the gyroscope drift upon reaching the limit of the required measuring accuracy. The objective is to connect the star sensor as infrequently as possible in order to conserve the limited energy resources of such satellites.
U.S. Pat. No. 6,732,977 B1 describes a method which is used to solve a further problem in the hybridization of star sensor data and gyroscope data. Since the gyroscope and the star sensor are not rigidly connected to one another, but instead are generally mounted at separate locations on the satellite, the fluctuation of the relative orientation of the two sensors must be additionally balanced for the hybridization. Thermoelastic effects caused by solar radiation are the main reason for mechanical distortions of the satellite. For this reason, in geocentrically viewing satellites the misalignment periodically changes with the orbit frequency. Use is made of this effect to ascertain the misalignment between the two sensors by frequency filtering corresponding to the orbit frequency. The misalignment is additionally integrated into the Kalman filter.
The prior art described thus far uses the hybridization of data of different AOCS sensors in order to balance the particular disadvantages of various types of sensors, such as the drift with gyroscopes or the noise with star sensors, with the respective other type. The aim is not to increase the measuring accuracy beyond the limit that is achievable using individual sensors. This additional task of sensor hybridization is provided in U.S. Pat. No. 7,062,363 B2.
The position measurement in an individual star sensor is based on the comparison of measured star positions to the positions from a star catalog. The catalog positions are expressed in an inertial coordinate system. The measurement takes place in the coordinate system associated with the sensor. For the position determination, the optimal transformation of all star positions from the inertial system into the sensor system is estimated. The more stars that are available, generally approximately 16, the greater the number of optimization equations that may be used for the position comparison. The accuracy of the position measurement increases with the number of equations used. U.S. Pat. No. 7,062,363 B2 is based on an increase in the number of available equations, in that the position estimation is determined not as an optimal transformation from the inertial system into the sensor system, but, rather, as a transformation from the inertial system into the coordinate system of the satellite body. For this purpose, initially the star positions measured by one or multiple star sensors are transformed into the satellite system. In addition, the star positions are predicted in satellite coordinates with the aid of the measured values of a gyroscope rate sensor. Corresponding to the increased number of stars which are present in all available star sensors, and the stars which are predicted using the rate sensor, a higher number of optimization equations, and thus enhanced accuracy, results.
The hybridization according to the method provided in U.S. Pat. No. 7,062,363 B2 has a better effect for the fusion of the data of two star sensors than for the fusion of the star sensor data with the data of the rate sensor. Star positions determined using multiple star sensors are statistically independent measurements, so that the measuring accuracy increases with the square root of the number of stars. The star positions predicted using the rate sensor are based not only on the measurement by the rate sensor, but also on previous measurements by the star sensors. Thus, the star positions are not statistically independent, and result in a slight improvement in the accuracy.
A hybridization of position data and rate data with the objective of improving accuracy is the subject matter of the article “Noise Estimation for Star Tracker Calibration and Enhanced Precision Attitude Determination,” Quang Lam, Craig Woodruff, and Sanford Ashton David Martin, in ISF 2002. In the present case, the base algorithm is the customary 6-dimensional EKF having the three position estimation errors and the three rate drift estimation errors as process parameters. Hybridization beyond that of the EKF is not provided. The aim is to achieve an improvement in accuracy by reducing the measuring errors to the component of the white noise. The measurements in the star sensor and in the gyroscope sensor also have other important correlated error components in addition to the white noise. White noise is a vital prerequisite for applicability of the EKF. Other noise components degrade the filtering result. The method described in the article “Noise Estimation for Star Tracker Calibration and Enhanced Precision Attitude Determination,” Quang Lam, Craig Woodruff, and Sanford Ashton David Martin, in ISF 2002 concerns the recognition and elimination of the non-white noise components of the position sensor and the rate sensor prior to the actual filtering.
The position measuring errors of star sensors and of integrating rate sensors contain, in addition to white noise (noise equivalent angle (NEA)), correlated errors having a high frequency (HF) or a low frequency (LF). In the star sensors, the HF errors are caused by high spatial frequency error (HSFE) noise. In contrast, the LF errors are caused by low spatial frequency error (LSFE) noise. In integrating rate sensors, low-frequency error components, which are characterized by the integrated angle error (angle random walk (ARW)) and the bias instability (BI), dominate.
The method according to the article “Noise Estimation for Star Tracker Calibration and Enhanced Precision Attitude Determination,” Quang Lam, Craig Woodruff, and Sanford Ashton David Martin, in ISF 2002 includes the recognition of the non-white noise components of both sensors in an identification step, and their elimination from the measured values and from the covariance matrices used in the EKF in a further, two-part deletion step. The recognition of the non-white error components is carried out independently for both types of sensors. The identification is not an integral part of the statistical estimation running in real time in the sensor data processing of the satellite. The identification takes place via complex post-processing of raw sensor data transmitted to the ground, with the aid of frequency filtering. The identification result is a numerical model (10th order polynomial) for the non-white (colored) noise components. Only this model is used in the on-board data processing.
The method described in “Noise Estimation for Star Tracker Calibration and Enhanced Precision Attitude Determination,” Quang Lam, Craig Woodruff, and Sanford Ashton David Martin, in ISF 2002 has major disadvantages. One disadvantage is the assumed continuous validity of the numerical colored error models. This may not be assumed in practice, so that continual recalibrations, including the ground segment of the satellite, are necessary. In addition to the loss of validity of the model of the star sensor over time, the star sensor model used has further undesirable constraints. In the publication, there is a requirement that the star sensor is mounted on the satellite in such a way that the stars pass diagonally through the image field. This is a requirement imposed on the design of the satellite and on the mission which cannot be met in broad-scale use of the star sensor. The underlying problem with star sensors is that the measuring error is a function of spatial frequencies, corresponding to the graphical evaluation, in which, however, time frequencies are used in the subsequent filtering and control. The conversion of the spatial frequencies into time frequencies is a function of time-variable parameters, such as the rotation rate and rotational direction. Therefore, a time model of the errors of a star sensor which is valid under all conditions of use is not possible in principle.
The adaptive extended Kalman filters (AEKFs), which are based on multiple model adaptive estimation (MMAE), represent a last group of relevant modifications of the EKF method. The aim of this method derivative is improved treatment of the second hidden Markov process, which is only indirectly reflected in the measurements. The hidden Markov process of the system behavior is determined by the control commands of the AOC system. It is possible under some circumstances for these commands to be explicitly delivered from the AOC to the AOD. Thus, the control commands could be treated as known variables in the Kalman filter of the AOD. For example, the AOC may notify the AOD in advance that a maneuver having a certain rotation rate will begin at a certain point in time. Other parameters of the hidden Markov process must be treated solely statistically. For example, the EKF must respond to a defect or a clear degradation of one of the sensors in such a way that no catastrophic consequences occur for the satellite control. For this example of error resistance, the EKF would run in parallel with multiple models of errors in the sensor system. Another example for the simultaneous use of multiple models is the taking into account of fluctuations of the operating voltage. These fluctuations influence the sensor measuring errors, but are not able to detect all of them by measurement. In this case, a model bank for voltage fluctuation ranges in the Kalman filter to be assumed could be used.
In addition to the customary recursive estimation of the system parameters and their errors via the EKF, for each of the models the MMAE estimation provides the probability that the model is valid at the instantaneous point in time. The estimation, the same as the EKF, recursively uses only the instantaneous measured values.
When a priori probabilities for the occurrence of certain model variants are present, these may be included in the determination of the probability of validity of the model variants. Either the estimation of that EKF having the highest probability of validity of the model or a weighted sum may be used as the end result.
The publication “Precision Attitude Determination Using a Multiple Model Adaptive Estimation Scheme,” Quang M. Lam, John L. Crassidis, in IEEE AC 2007 describes use of the MMAE technique with the aim of synergistic improvement in accuracy in the hybridization of data from multiple star sensors and an average-quality rate gyroscope for use in high-agility satellites. The objective is to achieve position accuracies which are orders of magnitude higher than the star sensor accuracy. It is shown that in mission phases having high rates, the 6-dimensional EKF traditionally used for the star sensor-gyroscope hybridization produces very large errors. The reason is the lack of accounting for the gyroscope scaling factor error and the gyroscope axis misalignment. These parameters must be taken into account at high rates. The difficulty to be overcome is that scale errors and drift errors of the gyroscope are not independent statistical variables.
Multiple model filtering is provided as a solution. Multiple EKF estimations run in parallel with different models. The models differ, on the one hand, by the dimensions of the vector of the system parameters. In addition to the mentioned six parameters, three parameters for the scaling factor error and six parameters for the gyroscope axis misalignment are introduced. Various 6-, 9-, and 15-dimensional EKF estimations are implemented in parallel. On the other hand, different models are used for different modes in which the star sensors may be present. A mode is defined, for example, by the star density in the viewing direction of the sensor, by the different rotation rates of the satellite, and by the more or less favorable orientation of the star sensor with respect to the satellite rotational axis. Probabilities which are known a priori are assumed for the modes. The weighted sum of all EKF estimations running in parallel applies as the overall estimation, the a priori probabilities of the modes and the reciprocal covariances of the differently dimensioned system models being used as weights.
Practical use of the above-described method would require considerable knowledge of various modes and their probabilities, which generally are not present. In addition, decorrelation of gyroscope drift errors and gyroscope scaling factor errors is not possible using the described approach.
The article “Multiple Model Adaptive Estimation of Satellite Attitude Using MEMS Gyros,” Hoday Stearns, Masayoshi Tomizuka, American Control Conference, 2011 likewise addresses the problem of improved estimation of the position based on the data of average-quality gyroscopes with the aid of EKF estimation. The two main parameters, ARW angle noise and BI drift, may not be assumed as constant for gyroscopes of this quality; instead, new estimations must continually be made. The reason for the change in these gyroscope parameters is considered to be their strong dependency on additional system parameters such as temperature or operating voltage. These system parameters are not known, and likewise must be estimated. As a solution, an MMAE scheme having a model bank of 49 different models is provided. For this purpose, the ARW noise and BI noise are each subdivided into seven different typical noise level classes. The combination results in the 49 EKF estimation processes which run in parallel, which are combined weighted with the probabilities of the validity of the noise level classes estimated in parallel. The problem of error correlation in all noise level classes used is not solved here.